| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 101 === When optimize placement of dampers for structures, the responses of structures must be obtained. But structures with supplemental dampers are often non-classically damped systems. Generally, these systems can be analyzed by direct integration methods like Newmark beta method or central difference method so that the responses of the structures can be obtained. If the degree-of-freedom of the structures is considerable, the direct integration methods are time consuming. So it affects computational efficiency of optimizing placement of dampers.
This study presents three current researches of mode superposition methods for the non-classically damped systems. The first two methods are developed by the uncoupled equations which base on the eigenvalue problem consists of mass, stiffness and damping matrices. The third method is developed by using the concept of eigen-decomposition and transforming the state-space equation of motion by Laplace Transform. Then the first method must pair the real eigenvalues of overdamped modes with each other and obtain the corresponding modal frequencies and modal damping ratios and finally superimpose these paired overdamped modes. The second and third methods just superimpose all the overdamped modes one by one. This study proves these three mode superposition methods are the same. And these mode superposition methods can develop the corresponding response spectrum methods so that can estimate the maximun response.
This study applies the mode superposition method, the corresponding response spectrum methods and the direct integration method to optimize placement of dampers for planar shear frames. The optimal method use the Simple method proposed by Leu et al. (2010). The optimal results by using the mode superposition method are the same as using the direct integration method. Furthermore, the mode superposition method provide less analysis time than the direct integration method.
For more real structures, this study applies mode superposition method direct integration method to optimize placement of dampers for two-way asymmetric buildings. At first degree-of-freedom of the structures must be simplified resonable, so use degree-of-freedom of the center of mass to describe the dynamic responses of the whole structures. And then use the software SAP 2000 to obtain mass and stiffness matrices of the structures. Damping matrices can be determined by geometric relationship. Finally, use the Simple method for the two-way asymmetric buildings. The optimal results by using the mode superposition method are the same as using the direct integration method. Furthermore, the mode superposition methods provide less analysis time than the direct integration methods.
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